Non-Cooperative Multi-Radio Channel Allocation in Wireless Networks

1
Non-Cooperative Multi-Radio Channel Allocation
in Wireless Networks

• Márk Félegyházi, Mario Cagalj, Shirin Saeedi
  Bidokhti, Jean-Pierre Hubaux
• Ecole Polytechnique Federale de Lausanne
  (EPFL), Lausanne, Switzerland
• University of Split, Croatia

Infocom 2007
2
Problem

• multi-radio devices
• set of available channels

How to assign radios to available channels?
3
System model (1/3)

• C set of orthogonal channels (C C)
• N set of communicating pairs of devices (N
  N)
• sender controls the communication (sender and
  receiver are synchronized)
• single collision domain if they use the same
  channel
• devices have multiple radios
• k radios at each device, k C

4
System model (2/3)

• N communicating pairs of devices
• C orthogonal channels
• k radios at each device

number of radios by sender i on channel x
?
Intuition
example
Use multiple radios on one channel ?
5
System model (3/3)

• channels with the same properties
• t t(kx) total throughput on any channel x
• t(kx) throughput per radio

6
Multi-radio channel allocation (MRCA) game

• selfish users (communicating pairs)
• non-cooperative game GMRCA
• players ? senders
• strategy ? channel allocation
• payoff ? total throughput
• strategy
• strategy matrix
• payoff

7
Game-Theoretic Concepts
Best response Best strategy of player i given
the strategies of others.
Nash equilibrium No player has an incentive to
unilaterally deviate.
Pareto-optimality The strategy profile spo is
Pareto-optimal if
with strict inequality for at least one player i
Price of anarchy The ratio between the total
payoff of players playing a socially-optimal
(max. Pareto-optimal) strategy and a worst Nash
equilibrium.
8
Use of all radios
Lemma If S is a NE in GMRCA, then
.
Each player should use all of his radios.
Intuition Player i is always better off
deploying unused radios.
all channel allocations
Lemma
9
Load-balancing channel allocation

• Consider two arbitrary channels x and y in C,
  where kx ky
• distance dx,y kx ky

Proposition If S is a NE in GMRCA, then dy,x
1, for any channel x and y.
all channel allocations
Lemma
Proposition
10
Nash equilibria (1/2)

• Consider two arbitrary channels x and y in C,
  where kx ky
• distance dx,y kx ky

• Theorem 1 A channel allocation S is a Nash
  equilibrium in GMRCA if for all i
• dx,y 1 and
• ki,x 1.

Nash Equilibrium
Use one radio per channel.
all channel allocations
NE type 1
Lemma
Proposition
11
Nash equilibria (2/2)

• Consider two arbitrary channels x and y in C,
  where kx ky
• distance dx,y kx ky
• loaded and less loaded channels C and C

• Theorem 2 A channel allocation S is a Nash
  equilibrium in GMRCA if
• dx,y 1,
• for any player i who has ki,x 2, x in C,
• for any player i who has ki,x 2 and x in C,
  ki,y ki,x 1, for all y in C

Nash Equilibrium
Use multiple radios on certain channels.
all channel allocations
NE type 1
Lemma
Proposition
C
C
NE type 2
12
Efficiency (1/2)
Theorem In GMRCA , the price of anarchy is
where
Corollary If tt(kx) is constant (i.e., ideal
TDMA), then any Nash equilibrium channel
allocation is Pareto-optimal in GMRCA.
13
Efficiency (2/2)

• In theory, if the total throughput function
  tt(kx) is constant ? POA 1
• In practice, there are collisions, but tt(kx)
  decreases slowly with kx (due to the RTS/CTS
  method)

G. Bianchi, Performance Analysis of the IEEE
802.11 Distributed Coordination Function, in
IEEE Journal on Selected Areas of Communication
(JSAC), 183, Mar. 2000
14
Summary

• wireless networks with multi-radio devices
• users of the devices are selfish players
• GMRCA multi-radio channel allocation game
• results for a Nash equilibrium
• players should use all their radios
• load-balancing channel allocation
• two types of Nash equilibria
• NE are efficient both in theory and practice
• fairness issues
• coalition-proof equilibria
• algorithms to achieve efficient NE
• centralized algorithm with perfect information
• distributed algorithm with imperfect information

http//people.epfl.ch/mark.felegyhazi
15
Future work

• general scenario conjecture hard
• approximation algorithms
• extend model to mesh networks (multihop
  communication)

16
Extensions
17
Related work

• Channel allocation
• in cellular networks fixed and dynamic Katzela
  and Naghshineh 1996, Rappaport 2002
• in WLANs Mishra et al. 2005
• in cognitive radio networks Zheng and Cao 2005
• Multi-radio networks
• mesh networks Adya et al. 2004, Alicherry et al.
  2005
• cognitive radio So et al. 2005
• Competitive medium access
• Aloha MacKenzie and Wicker 2003, Yuen and
  Marbach 2005
• CSMA/CA Konorski 2002, Cagalj et al. 2005
• WLAN channel coloring Halldórsson et al. 2004
• channel allocation in cognitive radio networks
  Cao and Zheng 2005, Nie and Comaniciu 2005

18
Fairness
Nash equilibria (unfair)
Nash equilibria (fair)
Theorem A NE channel allocation S is max-min
fair iff
Intuition This implies equality ui uj, ?i,j ?
N
19
Centralized algorithm
Assign links to the channels sequentially.
p4
p4
p4
p4
p2
p2
p3
p3
p3
p3
p2
p1
p1
p1
p1
p2
20
Convergence to NE (1/3)

• Algorithm with imperfect info
• move links from crowded channels to other
  randomly chosen channels
• desynchronize the changes
• convergence is not ensured

N 5, C 6, k 3
p5
p4
p5
p4
p3
p4
p3
p2
p5
p3
p1
p1
p2
p2
p1
time
p5 c2?c5
p1 c4?c6
c4
c5
channels
c1
c2
c3
c6
p1
p5
c6?c4
c5?c2
p4
p3
p3 c2?c5
p4 idle
p2
c6?c4
c1?c3
p1
p2 c2?c5
p1 c2?c5
c6?c4
21
Convergence to NE (2/3)

• Algorithm with imperfect info
• move links from crowded channels to other
  randomly chosen channels
• desynchronize the changes
• convergence is not ensured

Balance
best balance (NE)
unbalanced (UB)
Efficiency
22
Convergence to NE (3/3)